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CN116632509A - Rotary paraboloid type foldable antenna structure - Google Patents

Rotary paraboloid type foldable antenna structure Download PDF

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Publication number
CN116632509A
CN116632509A CN202310525937.XA CN202310525937A CN116632509A CN 116632509 A CN116632509 A CN 116632509A CN 202310525937 A CN202310525937 A CN 202310525937A CN 116632509 A CN116632509 A CN 116632509A
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China
Prior art keywords
freedom
degree
array
folding
foldable
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李君兰
李攀
张朝
王成
黄洪昌
张大卫
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Tianjin University
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Tianjin University
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/27Adaptation for use in or on movable bodies
    • H01Q1/28Adaptation for use in or on aircraft, missiles, satellites, or balloons
    • H01Q1/288Satellite antennas
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/08Means for collapsing antennas or parts thereof
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01QANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00Details of, or arrangements associated with, antennas
    • H01Q1/12Supports; Mounting means
    • H01Q1/1235Collapsible supports; Means for erecting a rigid antenna

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Astronomy & Astrophysics (AREA)
  • General Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Aerials With Secondary Devices (AREA)

Abstract

本发明公开一种旋转抛物面型可折展天线结构,基本单元基于刚性厚板剪纸理论设计,包括三个单自由度折展阵列、弹性驱动铰链与轮辐。弹簧驱动铰链安装在单自由度折展阵列的连接关节处,通过弹簧驱动可以实现折展阵列的自动展开。本发明通过材料切除与增添的方式对该折展阵列进行表面形貌处理,使得该阵列具有较高型面精度并通过板面之间、可折展阵列之间的干涉实现展开运动的停止。本发明在非工作状态能折叠成较小体积便于运输,在工作状态通过弹簧驱动力使可折展阵列展开至预期工作位置,具有结构简单,折展比大,自由度少,展开稳定,型面精度高等优点。

The invention discloses a rotating parabolic foldable antenna structure. The basic unit is designed based on the theory of rigid thick plate kirigami, and includes three single-degree-of-freedom foldable arrays, elastic drive hinges and spokes. The spring-driven hinge is installed at the connecting joint of the single-degree-of-freedom folding array, and the automatic unfolding of the folding array can be realized through spring driving. The present invention processes the surface topography of the expandable array by means of material removal and addition, so that the array has relatively high surface accuracy and realizes the stop of the unfolding motion through the interference between the board surfaces and the expandable array. The invention can be folded into a smaller volume in the non-working state for easy transportation, and in the working state, the foldable array can be unfolded to the expected working position by the driving force of the spring. The advantages of high surface accuracy.

Description

旋转抛物面型可折展天线结构Rotating Paraboloid Foldable Antenna Structure

技术领域technical field

本发明涉及空间可折展机构技术领域,特别是涉及一种旋转抛物面型可折展天线结构。The invention relates to the technical field of space foldable mechanisms, in particular to a rotating parabolic foldable antenna structure.

背景技术Background technique

空间可展结构是实现空间飞行器主结构、次结构或某一部件由初始位置或形态,变化到最终位置或形态,并保持该状态的结构。它是伴随着航天器发展,由简单到复杂逐步发展起来的一个结构领域。随着航天领域飞速发展,诞生了具有可展开特性的大型航天结构,这种类型可展结构在发射过程中处于折叠收拢状态,固定安装在运载火箭内部,发射入轨后,由地面指挥中心控制结构按照要求逐渐展开,锁定后保持工作运行状态,从而形成一大型空间结构。抛物型面可展固面天线是空间可展结构在航天工程中的一个重要应用,受到很多研究人员重视,是卫星结构重要组成部分,是直接执行卫星功能的重要物理平台。The space deployable structure is a structure that realizes the change of the main structure, secondary structure or a certain part of the spacecraft from the initial position or shape to the final position or shape, and maintains this state. It is a structural field gradually developed from simple to complex with the development of spacecraft. With the rapid development of the aerospace field, large-scale aerospace structures with expandable characteristics have been born. This type of expandable structure is in a folded and folded state during launch, and is fixedly installed inside the launch vehicle. After launching into orbit, it is controlled by the ground command center. The structure unfolds gradually according to the requirements, and keeps working and running after locking, thus forming a large-scale space structure. Parabolic deployable fixed surface antenna is an important application of space deployable structure in aerospace engineering, and it has attracted the attention of many researchers. It is an important part of satellite structure and an important physical platform that directly performs satellite functions.

目前,国内外研究学者已经对固面可展结构进行了很多研究,设计出了多种类型可展固面结构。固面可展机构普遍由刚性厚板形成工作型面,使用铰链作为刚性面板间旋转关节,在非工作时折叠收拢,工作时依靠驱动铰链或电机缓慢打开,支撑结构如桁架等。现有固面可展结构如向日葵形折展天线、卡塞格伦折展天线等,具有高型面精度、结构稳定的特点,然而其折展比小,难以满足当前和未来的使用需求。因此,设计具有少自由度、结构简单、较大折展比和较高型面精度的可展固面结构是研究人员重点关注的问题。At present, researchers at home and abroad have conducted a lot of research on the solid-surface deployable structure, and have designed various types of deployable solid-surface structures. The solid surface expandable mechanism generally forms the working surface by rigid thick plates, using hinges as the rotating joints between the rigid panels, which are folded and folded when not working, and slowly opened by driving hinges or motors when working, and supporting structures such as trusses. Existing fixed-surface deployable structures, such as sunflower-shaped foldable antennas and Cassegrain foldable antennas, have the characteristics of high surface accuracy and stable structure, but their fold-to-brow ratio is small, which makes it difficult to meet current and future use requirements. Therefore, designing a developable solid-surface structure with few degrees of freedom, simple structure, large fold-to-expand ratio, and high surface accuracy is the focus of researchers.

发明内容Contents of the invention

本发明的目的是针对现有技术中的问题,而提供一种具有大折展比、高型面精度、高稳定性的优点的旋转抛物面型可折展天线结构,旨在解决当前空间可展结构折展比小、型面精度低或是无法自主展开的问题。The purpose of the present invention is to solve the problems in the prior art, and provide a rotating parabolic foldable antenna structure with the advantages of large folding ratio, high profile precision, and high stability, aiming at solving the problem of the current space expandable antenna structure. Problems with small structural expansion ratio, low surface accuracy or inability to expand independently.

为实现本发明的目的所采用的技术方案是:The technical scheme adopted for realizing the purpose of the present invention is:

一种旋转抛物面型可折展天线结构,包括由多个相同的单自由度折展阵列和一个轮辐组成,轮辐位于可展天线结构的中间,多个单自由度折展阵列绕轮辐中心线间隔一定角度排布;单个单自由度折展阵列由多个基本折展单元交替排布构成,每个基本折展单元由刚性厚板通过第一弹簧驱动铰链连接构成;每个单自由度折展阵列与轮辐之间由第二弹簧驱动铰链连接;可折展天线结构展开至工作状态时,单自由度可展阵列的侧边彼此相对应;所述刚性厚板的表面形貌进行材料增添和切除处理,调整二面角或扇形角制定曲面曲率,使刚性厚板具有预定型面,以满足型面和自锁要求。A rotating parabolic deployable antenna structure, including multiple identical single-degree-of-freedom deployable arrays and a spoke, the spoke is located in the middle of the deployable antenna structure, and multiple single-degree-of-freedom deployable arrays are spaced around the centerline of the spoke Arranged at a certain angle; a single single-degree-of-freedom folding array is composed of multiple basic folding units arranged alternately, and each basic folding unit is composed of a rigid thick plate connected by a first spring-driven hinge; each single-degree-of-freedom folding The array and the spokes are connected by a second spring-driven hinge; when the expandable antenna structure is unfolded to the working state, the sides of the single-degree-of-freedom expandable array correspond to each other; the surface topography of the rigid plate is added and Excision processing, adjusting the dihedral angle or sector angle to formulate the curvature of the surface, so that the rigid thick plate has a predetermined profile to meet the profile and self-locking requirements.

其中,多个所述单自由度折展阵列的结构完全相同。Wherein, the structures of the multiple single-degree-of-freedom unfolding arrays are completely the same.

其中,所述单自由度折展阵列由第一基本折展单元、第二基本折展单元以及第三基本折展单元构成;第一基本折展单元紧挨所述轮辐对称布置,顺序排列;第二基本折展单元在第一基本折展单元的上方排列;第三基本折展单元位于第一基本折展单元与第二基本折展单元之间,且第一基本折展单元与第二基本折展单元交错排列,共用刚性厚板。Wherein, the single-degree-of-freedom folding array is composed of a first basic folding unit, a second basic folding unit, and a third basic folding unit; the first basic folding unit is symmetrically arranged next to the spokes, and arranged sequentially; The second basic folding unit is arranged above the first basic folding unit; the third basic folding unit is located between the first basic folding unit and the second basic folding unit, and the first basic folding unit and the second basic folding unit The basic folding units are arranged in a staggered manner and share a rigid slab.

其中,当所述单自由度折展阵列展开为平面且所述刚性厚板的列数确定时,通过调整扇形角大小计算阵列数量,使得多个所述单自由度折展阵列展开形成闭环,从而制定曲面曲率。Wherein, when the single-degree-of-freedom folding array is unfolded into a plane and the number of columns of the rigid thick plate is determined, the number of arrays is calculated by adjusting the fan angle, so that multiple single-degree-of-freedom folding arrays are unfolded to form a closed loop, Thus formulating the curvature of the surface.

其中,当所述单自由度折展阵列的二面角确定时,通过调整二面角大小来制定曲面曲率。Wherein, when the dihedral angle of the single-degree-of-freedom unfolded array is determined, the curvature of the surface is formulated by adjusting the size of the dihedral angle.

其中,所述单自由度折展阵列的基本折展单元的中间下板的正面梯形底边\背面梯形底边与轮辐的正面边线相连,分别形成第一装配构型与第二装配构型。Wherein, the front trapezoidal base/back trapezoidal base of the middle lower plate of the basic folding unit of the single-degree-of-freedom folding array are connected to the front side of the spokes to form a first assembly configuration and a second assembly configuration respectively.

其中,所述基本折展单元的中间下板的正面梯形底边与轮辐的正面边线相连形成第一装配构型;所述第一装配构型在所述单自由度折展阵列同步运动时,展开至工作状态时呈现旋转抛物面形状,且切割出完整目标旋转抛物面,收拢时轨迹呈单自由度运动。Wherein, the front trapezoidal base of the middle lower plate of the basic folding unit is connected to the front edge of the spokes to form a first assembly configuration; when the single-degree-of-freedom folding array moves synchronously, the first assembly configuration, When unfolded to the working state, it presents the shape of a rotating paraboloid, and cuts out a complete target rotating paraboloid, and when it is folded, the trajectory is a single-degree-of-freedom movement.

其中,所述基本折展单元的中间下板的正面梯形底边与轮辐的背面边线相连形成第二装配构型;所述第二装配构型在所述单自由度折展阵列同步运动时,展开时呈现抛旋转物面形状,收拢完成后,有两种不同状态,所述两种状态能相互转换。Wherein, the front trapezoidal base of the middle lower plate of the basic folding unit is connected to the rear edge of the spokes to form a second assembly configuration; when the single-degree-of-freedom folding array moves synchronously, the second assembly configuration, When unfolded, it presents the shape of a parabolic plane of rotation, and after being folded, it has two different states, and the two states can be converted to each other.

其中,通过去除材料使所述刚性厚板的型面与目标抛物面匹配,通过增添材料使所述刚性厚板在展开至工作位置时与相邻刚性厚板相接触,从而实现所述单自由度折展阵列在弹簧驱动铰链与刚性厚板间接触力的共同作用下能保持在工作位置,且所述刚性厚板的型面与目标抛物面相匹配,形成具有大折展比、高型面精度、高稳定性的旋转抛物面型可折展结构。Wherein, the profile of the rigid slab matches the target paraboloid by removing material, and the single degree of freedom is realized by adding material to make the rigid slab contact with the adjacent rigid slab when unfolded to the working position The folding array can be kept in the working position under the combined action of the contact force between the spring-driven hinge and the rigid thick plate, and the profile of the rigid thick plate matches the target paraboloid, forming a large folding-expanding ratio and high profile accuracy , High stability rotating paraboloid foldable structure.

其中,所述单自由度可展阵列的截面形态为以梯度的形式在阶梯斜坡中上升,当截面倾角与抛物线倾角匹配时,通过对所述刚性厚板进行材料的去除和增添使得刚性厚板的型面实现与目标抛物面匹配。Wherein, the cross-sectional shape of the single-degree-of-freedom expandable array is to rise in the form of a gradient, and when the inclination angle of the section matches the inclination angle of the parabola, removing and adding materials to the rigid thick plate makes the rigid thick plate The profile is matched with the target paraboloid.

本发明的旋转抛物面型可折展天线结构,基于厚板剪纸折叠方式设计单自由度可展阵列,通过单自由度折展阵列与轮辐的连接,经过刚性厚板的型面调整后,在弹簧驱动铰链的驱动力下实现了可折展结构的展开,在驱动力与接触力共同作用下展开至工作位置,实现了工作时的特定抛物线型型面要求。The rotating parabolic foldable antenna structure of the present invention is based on the design of a single-degree-of-freedom deployable array based on the paper-cut folding method of a thick plate. Through the connection between the single-degree-of-freedom foldable array and the spokes, after the profile adjustment of the rigid thick plate, the spring The unfolding of the foldable structure is realized under the driving force of the driving hinge, and it is unfolded to the working position under the joint action of the driving force and the contact force, and the specific parabolic profile requirements during work are realized.

附图说明Description of drawings

图1是本发明实施例的旋转抛物面型可折展天线结构展开后轴测示意图。Fig. 1 is a schematic diagram of a perspective view of a rotating parabolic foldable antenna structure according to an embodiment of the present invention after unfolding.

图2是本发明实施例的旋转抛物面型可折展天线结构展开后俯视第一示意图(展示三个单自由度折展阵列的布置方式)。Fig. 2 is a first top view of the rotating parabolic foldable antenna structure of the embodiment of the present invention after unfolding (showing the arrangement of three single-degree-of-freedom foldable arrays).

图3是本发明实施例的旋转抛物面型可折展天线结构展开后俯视第二示意图(展示每个单自由度可展阵列的五个基本折展单元布置方式)。Fig. 3 is a second schematic diagram of the rotating parabolic foldable antenna structure unfolded according to the embodiment of the present invention (showing the arrangement of five basic foldable units of each single-degree-of-freedom deployable array).

图4是本发明实施例的单自由度折展阵列的示意图。Fig. 4 is a schematic diagram of a single-degree-of-freedom unfolding array according to an embodiment of the present invention.

图5是本发明实施例的弹簧驱动铰链的示意图。Fig. 5 is a schematic diagram of a spring-actuated hinge according to an embodiment of the present invention.

图6是本发明实施例基本折展单元的六个厚板的角度及厚度参数示意图。Fig. 6 is a schematic diagram of the angle and thickness parameters of the six thick plates of the basic folding unit according to the embodiment of the present invention.

图7是本发明实施例带弹簧驱动铰链的基本折展单元的正面示意图。Fig. 7 is a schematic front view of a basic folding unit with a spring-driven hinge according to an embodiment of the present invention.

图8是本发明实施例带弹簧驱动铰链的基本折展单元的背面示意图。Fig. 8 is a schematic rear view of a basic folding unit with spring-driven hinges according to an embodiment of the present invention.

图9是本发明实施例的单自由度折展阵列的分割裁切示意图。FIG. 9 is a schematic diagram of division and cutting of a single-degree-of-freedom unfolding array according to an embodiment of the present invention.

图10是本发明实施例的旋转抛物面型可折展天线结构目标型面的正面示意图。Fig. 10 is a schematic front view of a target profile of a rotating parabolic foldable antenna structure according to an embodiment of the present invention.

图11是本发明实施例的旋转抛物面型可折展天线结构目标型面的反面示意图。Fig. 11 is a schematic view of the reverse side of the target profile of the rotating parabolic foldable antenna structure according to the embodiment of the present invention.

图12是本发明实施例的旋转抛物面型可折展天线结构目标型面处理示意图。Fig. 12 is a schematic diagram of target profile processing of a rotating parabolic foldable antenna structure according to an embodiment of the present invention.

图13是本发明实施例的旋转抛物面型可折展天线结构的两种不同安装形式的装配构型示意图。Fig. 13 is a schematic diagram of the assembly configuration of two different installation forms of the rotating parabolic foldable antenna structure according to the embodiment of the present invention.

图14是本发明实施例旋转抛物面型可折展天线结构的展开过程示意图。Fig. 14 is a schematic diagram of the unfolding process of the rotating parabolic foldable antenna structure according to the embodiment of the present invention.

附图标记:Reference signs:

1单自由度折展阵列、2轮辐;1 single degree of freedom folding array, 2 spokes;

I第一单自由度可展阵列、Ⅱ第二单自由度可展阵列、Ⅲ第三单自由度可展阵列;I first single degree of freedom expandable array, II second single degree of freedom expandable array, III third single degree of freedom expandable array;

1-1第一基本折展单元,1-2第二基本折展单元,1-3第三基本折展单元,1-4第四基本折展单元,1-5基本折展单元;1-1 first basic folding unit, 1-2 second basic folding unit, 1-3 third basic folding unit, 1-4 fourth basic folding unit, 1-5 basic folding unit;

2-1第一板,2-2第二板,2-3第三板,2-4第四板,2-5第五板,2-6第六板,2-7第七板,2-8第八板,2-9第九板,2-10第十板,2-11第十一板,2-12第十二板,2-13第十三板,2-14第十四板,2-15第十五板,2-16第十六板,2-17第十七板,2-18第十八板,2-19第十九板,2-20第二十板2-20;2-1 first plate, 2-2 second plate, 2-3 third plate, 2-4 fourth plate, 2-5 fifth plate, 2-6 sixth plate, 2-7 seventh plate, 2 -8 eighth plate, 2-9 ninth plate, 2-10 tenth plate, 2-11 eleventh plate, 2-12 twelfth plate, 2-13 thirteenth plate, 2-14 fourteenth plate Plate, 2-15 fifteenth plate, 2-16 sixteenth plate, 2-17 seventeenth plate, 2-18 eighteenth plate, 2-19 nineteenth plate, 2-20 twentieth plate 2 -20;

3-1弹簧铰链左合页、3-2弹簧铰链右合页、3-3弹簧及销轴、3-4固定螺栓孔;3-1 Spring hinge left hinge, 3-2 Spring hinge right hinge, 3-3 Spring and pin, 3-4 Fixing bolt holes;

4-1第一装配构型、4-2第二装配构型。4-1 first assembly configuration, 4-2 second assembly configuration.

具体实施方式Detailed ways

以下结合附图和具体实施例对本发明作进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

本发明的旋转抛物面型可折展天线结构,由三个相同的单自由度可折展单元及一个轮辐构成,通过对刚性厚板材料的增添或去除获取理想的工作型面,通过弹性驱动铰链驱动整体结构的展开。The rotating parabolic foldable antenna structure of the present invention is composed of three identical single-degree-of-freedom foldable units and a spoke. The ideal working surface is obtained by adding or removing rigid thick plate materials, and the hinge is driven elastically. Drive the unfolding of the overall structure.

参考图1所示,一种旋转抛物面型可折展天线结构,基于剪纸理论以及平面剪纸的厚板化设计而成,由弹簧驱动铰链和单自由度折展阵列单元1连接构成,具体的,参见图2所示,由三个相同的第一单自由度折展阵列I、第二单自由度折展阵列II、第三单自由度折展阵列III及一个轮辐2构成,每个单自由度折展阵列由二十块刚性厚板及二十八个弹性驱动铰链(正面有16个,背面有12个)构成,每个单自由度折展阵列与轮辐之间由两个额外的弹簧驱动铰链连接,如所述单自由度折展阵列I、单自由度折展阵列II、单自由度折展阵列III各自通过两个弹簧驱动铰链与轮辐连接。采用材料增添和切除方式对刚性厚板的表面形貌进行处理,使得刚性厚板具有特定的预设型面,并利用刚性厚板的板面之间的干涉实现展开状态的运动停止,从而满足型面和自锁要求。Referring to Figure 1, a rotating parabolic foldable antenna structure is designed based on kirigami theory and planar kirigami thickening, and is composed of a spring-driven hinge and a single-degree-of-freedom foldable array unit 1. Specifically, As shown in Figure 2, it consists of three identical first single-degree-of-freedom deployment arrays I, second single-degree-of-freedom deployment arrays II, third single-degree-of-freedom deployment arrays III and a spoke 2, each single-degree-of-freedom The single-degree-of-freedom array consists of twenty rigid slabs and twenty-eight elastically driven hinges (16 on the front and 12 on the back), with two additional springs between each single-degree-of-freedom array and the spokes Driving hinge connection, for example, the single-degree-of-freedom folding array I, the single-degree-of-freedom folding array II, and the single-degree-of-freedom folding array III are connected to the spokes through two spring-driven hinges. The surface morphology of the rigid slab is processed by material addition and removal, so that the rigid slab has a specific preset profile, and the movement of the unfolded state is stopped by using the interference between the surfaces of the rigid slab to meet the requirements Profile and self-locking requirements.

本申请实施例中,对于单自由度折展阵列以及所述轮辐,可以使用3D打印的技术进行等比模型制作,加工材料可以为PLA,使用此种加工方法以及材料,使得加工简单,重量较轻且成本较低。In the embodiment of the present application, for the single-degree-of-freedom folding array and the spokes, 3D printing technology can be used to make a scale model, and the processing material can be PLA. Using this processing method and material makes the processing simple and the weight is relatively low. Light and low cost.

该旋转抛物面型可折展天线结构整体,从俯视角度观察,轮辐位于可展结构的中间,所述的第一单自由度折展阵列I、第二单自由度折展阵列Ⅱ、第三单自由度折展阵列Ⅲ绕所述的轮辐的中心线间隔120°排布,如图2所示,每个单自由度折展阵列按轮辐的中心线间隔120°分割裁切,请参见图9所示,除去两侧的虚线部分,形成一个所述单自由度折展阵列。The whole structure of the rotating parabolic foldable antenna is viewed from a top view, and the spokes are located in the middle of the deployable structure. The first single-degree-of-freedom foldable array I, the second single-degree-of-freedom foldable array II, and the third single-degree The degree of freedom folding array III is arranged at intervals of 120° around the centerline of the spokes, as shown in Figure 2, and each single degree of freedom folding array is divided and cut according to the centerline of the spokes at intervals of 120°, see Figure 9 As shown, the dotted line parts on both sides are removed to form a single-degree-of-freedom unfolded array.

本申请实施例中,所述弹簧驱动铰链由左合页3-1、右合页3-2、驱动弹簧及连接销轴3-3和螺栓3-4组成,所述左合页与右合页通过连接销轴连接,所述驱动弹簧嵌套于连接销轴之上,所述驱动弹簧的簧丝末端分别与左合页、右合页接触,提供驱动力,所述弹簧驱动铰链位于刚性厚板关节处,左合页、右合页与刚性板相连,以此构成具有驱动作用的旋转运动副,如图5所示。In the embodiment of the present application, the spring-driven hinge is composed of a left hinge 3-1, a right hinge 3-2, a driving spring, a connecting pin 3-3 and a bolt 3-4, and the left hinge and the right hinge The pages are connected by connecting pins, the driving spring is nested on the connecting pin, and the spring wire ends of the driving spring are respectively in contact with the left hinge and the right hinge to provide driving force, and the spring driving hinge is located on the rigid At the joint of the thick plate, the left hinge and the right hinge are connected with the rigid plate to form a rotating motion pair with a driving effect, as shown in Figure 5.

本发明实施例中,所述弹簧驱动铰链为金属制作,安装在单自由度可展阵列的折痕位置,具有强度高,质量轻的优点。In the embodiment of the present invention, the spring-driven hinge is made of metal, installed at the crease position of the single-degree-of-freedom expandable array, and has the advantages of high strength and light weight.

作为一个实施例,三个所述单自由度折展阵列的结构完全相同,每个可折展阵列由多个基本折展单元构成,作为一个实施例,由五个基本折展单元构造出一个单自由度折展阵列,构造出后需要对部分刚性厚板进行裁切,以保证折叠后也不发生干涉。As an example, the structures of the three single-degree-of-freedom expandable arrays are identical, and each expandable array is composed of a plurality of basic expandable units. As an example, five basic expandable units are used to construct a For single-degree-of-freedom folding arrays, some rigid thick plates need to be cut after construction to ensure that no interference occurs after folding.

参见图3所示,其中,第一基本折展单元1-1和第二基本折展单元1-2对称布置排列,第四基本折展单元1-4和第五基本折展单元1-5在第一基本折展单元1-1和第二基本折展单元1-2的上方对称布置排列,第三基本折展单元1-3位于第一基本折展单元1-1、第二基本折展单元1-2、第四基本折展单元1-4和第五基本折展单元1-5之间,如图3所示,第二基本折展单元1-2在第一基本折展单元1-1的右侧,其与第一基本折展单元1-1有两块共用板;第四基本折展单元1-4在第一基本折展单元1-1的上方,与第一基本折展单元1-1无共用板;第五基本折展单元1-5在第二基本折展单元1-2上方,与第二基本折展单元1-2无共用板;第三基本折展单元1-3位于第一基本折展单元1-1、第二基本折展单元1-2、第四基本折展单元1-4、第五基本折展单元1-5的中间,与第一基本折展单元1-1、第二基本折展单元1-2、第四基本折展单元1-4、第五基本折展单元1-5有六块共用板。Referring to Fig. 3, wherein, the first basic folding unit 1-1 and the second basic folding unit 1-2 are arranged symmetrically, the fourth basic folding unit 1-4 and the fifth basic folding unit 1-5 Arranged symmetrically above the first basic folding unit 1-1 and the second basic folding unit 1-2, the third basic folding unit 1-3 is located at the first basic folding unit 1-1, the second basic folding unit Between the display unit 1-2, the fourth basic folding unit 1-4 and the fifth basic folding unit 1-5, as shown in Figure 3, the second basic folding unit 1-2 is in the first basic folding unit 1-1 on the right side, it has two common boards with the first basic folding unit 1-1; the fourth basic folding unit 1-4 is above the first basic folding unit 1-1, and the first basic The folding unit 1-1 has no common plate; the fifth basic folding unit 1-5 is above the second basic folding unit 1-2, and has no common board with the second basic folding unit 1-2; the third basic folding unit Unit 1-3 is located in the middle of the first basic folding unit 1-1, the second basic folding unit 1-2, the fourth basic folding unit 1-4, and the fifth basic folding unit 1-5. The basic folding unit 1-1, the second basic folding unit 1-2, the fourth basic folding unit 1-4, and the fifth basic folding unit 1-5 have six common boards.

其中,参见图4所示,每个所述基本折展单元由六块板连接构成,如第一基本折展单元1-1的组成板为第三板2-3、第四板2-4、第七板2-7、第八板2-8、第十一板2-11,第十二板2-12,如第二基本折展单元1-2的组成板为第十一2-11、第十二板2-12、第十五板2-15、第十六板2-16、第十九板2-19、第二十板2-20;第一基本折展单元1-1与第二基本折展单元1-2共用第十一板2-11和第十二板2-12,参见图6所示,其它三个基本折展单元的结构不再赘述,请参见图4所示。Wherein, as shown in FIG. 4, each of the basic folding units is composed of six connected plates, such as the first basic folding unit 1-1 composed of a third plate 2-3 and a fourth plate 2-4. , the seventh plate 2-7, the eighth plate 2-8, the eleventh plate 2-11, the twelfth plate 2-12, such as the composition plate of the second basic folding unit 1-2 is the eleventh 2- 11. The twelfth board 2-12, the fifteenth board 2-15, the sixteenth board 2-16, the nineteenth board 2-19, the twentieth board 2-20; the first basic folding unit 1- 1 and the second basic folding unit 1-2 share the eleventh board 2-11 and the twelfth board 2-12, as shown in Figure 6, the structures of the other three basic folding units will not be described in detail, please refer to Figure 4.

参见图4所示,以左侧的一个基本折展单元为例,其中间上下相连布置两个中间板,中间板的两侧各布置二个外侧板,它们相互连接形成所述基本折展单元;每个所述基本折展单元的峰折痕设置在其厚板单元的左第一板(第三板2-3)和中间第一板(第七板2-7)连接处、左第二板(第四板2-4)和中间第二板(第八板2-8)连接处、中间第一板(第七板2-7)和右第一板(第十一板2-11)连接处、中间第二板(第八板2-8)和右第二板(第十二板2-12)连接处,谷折痕设置在厚板单元左第一板(第三板2-3)和左第二板(第四板2-4)连接处、右第一板(第十一板2-11)和在第二板(第十二板2-12)连接处。Referring to Figure 4, taking a basic folding unit on the left as an example, two middle plates are connected up and down in the middle, and two outer plates are arranged on both sides of the middle plate, and they are connected to each other to form the basic folding unit ; The peak creases of each of the basic folding units are arranged at the junction of the left first plate (the third plate 2-3) and the middle first plate (the seventh plate 2-7) of the thick plate unit, and the left first plate (the seventh plate 2-7). The connection between the second board (the fourth board 2-4) and the middle second board (the eighth board 2-8), the middle first board (the seventh board 2-7) and the right first board (the eleventh board 2- 11) At the joint, the joint of the middle second plate (the eighth plate 2-8) and the right second plate (the twelfth plate 2-12), the valley crease is set on the left first plate (the third plate 2-3) at the junction of the left second board (fourth board 2-4), right first board (eleventh board 2-11) and at the junction of the second board (twelfth board 2-12).

如图6所示,对于任一基本折展单元,在满足厚板折纸的约束条件下才能正常折展,基本折展单元由两个单顶点四折痕共用一条折痕构成,角度关系应满足:α1+α2=π,α3+α4=π,α5+α7=π,α6+α8=π,板厚关系应满足a1=a3=a5=A1,a2=a4=a6=A2, As shown in Figure 6, for any basic folding unit, it can be folded normally only when the constraints of thick plate origami are met. The basic folding unit is composed of two single-vertex four-fold creases sharing one crease, and the angle relationship should satisfy : α1+α2=π, α3+α4=π, α5+α7=π, α6+α8=π, the plate thickness relationship should satisfy a1=a3=a5=A1, a2=a4=a6=A2,

上述参数中,a1~a6是板厚,α1~α8是扇形角,以基本折展单元1-1为例解释参数含义,a1为第四板2-4的厚度,a2为第八板2-8的厚度,a3为第十二板2-12的厚度,a4为第三板2-3的厚度,a5为第七板2-7的厚度,a6为第十一板2-11的厚度,α1为第四板2-4正面梯形中顶边与右斜边之间的夹角,α2为第八板2-8正面梯形中顶边与左斜边之间的夹角,α3为第七板2-7正面梯形中底边与左斜边之间的夹角,α4为第三板2-3正面梯形中底边与右斜边之间的夹角,α5为第八板2-8正面梯形中顶边与右斜边之间的夹角,α6为第十二板2-12正面梯形中顶边与左斜边之间的夹角,α7为第十一板2-11正面梯形中底边与左斜边之间的夹角,α8为第七板2-7正面梯形中底边与右斜边之间的夹角。Among the above parameters, a1~a6 are plate thicknesses, α1~α8 are sector angles, take the basic folding unit 1-1 as an example to explain the meaning of parameters, a1 is the thickness of the fourth plate 2-4, a2 is the eighth plate 2- 8, a3 is the thickness of the twelfth board 2-12, a4 is the thickness of the third board 2-3, a5 is the thickness of the seventh board 2-7, a6 is the thickness of the eleventh board 2-11, α1 is the angle between the top side and the right hypotenuse in the front trapezoid of the fourth board 2-4, α2 is the included angle between the top side and the left hypotenuse in the front trapezoid of the eighth board 2-8, and α3 is the seventh The angle between the bottom edge and the left hypotenuse of the front trapezoid of plate 2-7, α4 is the angle between the bottom edge and the right hypotenuse of the front trapezoid of plate 2-3, and α5 is the angle between the bottom edge and the right hypotenuse of the eighth plate 2-8 The angle between the top side and the right hypotenuse of the front trapezoid, α6 is the angle between the top side and the left hypotenuse of the front trapezoid of the twelfth board 2-12, and α7 is the front trapezoid of the eleventh board 2-11 The angle between the bottom edge and the left hypotenuse, α8 is the angle between the bottom edge and the right hypotenuse of the front trapezoid of the seventh plate 2-7.

其中,对于每个基本折展单元,相邻厚板间共有6个旋转关节,每个旋转关节安装1个或2个弹簧驱动铰链,参见图7、图8所示,图中有6个旋转关节,关节上共有8个弹簧驱动铰链,为了提高刚度,其背面每个关节分别都使用了两个弹簧驱动铰链,从正面观察,弹簧驱动铰链的安装位置有左第一板右斜边与中间第一板左斜边的连接处、左第二板右斜边与中间第二板左斜边的连接处、右第一板左斜边与中间第一板右斜边的连接处、右第二板左斜边与中间第二板右斜边的连接处,从背面观察,弹簧驱动铰链的安装位置有左第一板下平边与左第二板上平边的连接处、右第一板下平边与右第二板上平边的连接处。Among them, for each basic folding unit, there are 6 rotating joints between adjacent thick plates, and each rotating joint is equipped with 1 or 2 spring-driven hinges, as shown in Figure 7 and Figure 8, and there are 6 rotating joints in the figure. Joints, there are 8 spring-driven hinges on the joints. In order to improve the rigidity, each joint on the back uses two spring-driven hinges. Viewed from the front, the installation positions of the spring-driven hinges are the left first plate, the right hypotenuse and the middle The junction of the left hypotenuse of the first board, the junction of the right hypotenuse of the second left board and the left hypotenuse of the middle second board, the junction of the left hypotenuse of the right first board and the right hypotenuse of the middle first board, the right The connection between the left hypotenuse of the second plate and the right hypotenuse of the middle second plate, viewed from the back, the installation position of the spring-driven hinge is the connection between the lower flat edge of the left first plate and the flat edge of the left second plate, and the right first plate The connection between the lower flat edge and the flat edge on the second right plate.

本申请实施例的可折展天线结构,在展开至工作状态时,三个单自由度可展阵列的侧边彼此相对应。三个单自由度折展阵列独立同步展开,对于任一所述单自由度折展阵列,仅需要一个驱动力即可实现阵列的折叠运动,例如运动输入由单自由度的第一基本折展单元1-1传递至单自由度的第二基本折展单元1-2,再由单自由度的第二基本折展单元1-2传递至单自由度的第三基本折展单元1-3,再由单自由度的第三基本折展单元1-3传递至单自由度的第四基本折展单元1-4,再由单自由度的第四基本折展单元1-4传递至单自由度的第五基本折展单元1-5。通过所述弹簧驱动铰链为单自由折展阵列展开至工作位置提供驱动力,其余位置提供辅助展开力,帮助单自由折展阵列实现折叠运动。In the foldable antenna structure of the embodiment of the present application, when unfolded to the working state, the sides of the three single-degree-of-freedom deployable arrays correspond to each other. The three single-degree-of-freedom folding arrays are independently and synchronously deployed. For any one of the single-degree-of-freedom folding arrays, only one driving force is needed to realize the folding movement of the array. The unit 1-1 is transferred to the second basic folding unit 1-2 with a single degree of freedom, and then the second basic folding unit 1-2 with a single degree of freedom is transferred to the third basic folding unit 1-3 with a single degree of freedom , and then transferred from the third basic folding unit 1-3 with a single degree of freedom to the fourth basic folding unit 1-4 with a single degree of freedom, and then transferred to the single The fifth basic folding unit 1-5 of the degree of freedom. The spring-driven hinge provides a driving force for the single freely deployable array to unfold to a working position, and other positions provide auxiliary unfolding force to help the single freely deployable array realize folding movement.

本发明的可折展天线结构,是由多个相同的单自由度折展阵列构造成可展天线结构,为了形成旋转抛物面,需要通过多个基本折展单元构成单自由度可展阵列,其中的数学关系可描述为:The deployable antenna structure of the present invention is a deployable antenna structure constructed of multiple identical single-degree-of-freedom deployable arrays. In order to form a rotating paraboloid, it is necessary to form a single-degree-of-freedom deployable array through a plurality of basic deployable units. The mathematical relationship of can be described as:

其中,m为单自由度折展阵列的数量,代表相邻刚性厚板的二面角,mR为单自由度可展阵列中绕轮辐中心选装方向的厚板层数。Among them, m is the number of single-degree-of-freedom folding arrays, Represents the dihedral angle of adjacent rigid slabs, m R is the number of slab layers in the optional direction around the center of the spoke in the single-degree-of-freedom expandable array.

本发明实施例的旋转抛物面型可折展天线结构可以采用两种方式实现设计同样的抛物面,第一种是通过调整扇形角α1~α8来达到设计要求,第二种是通过调整二面角来达到设计要求。通过对旋转抛物面型可折展天线结构的刚性厚板进行材料的增添或去除就可以得到目标抛物面,如图10、图11所示。The rotating parabolic foldable antenna structure of the embodiment of the present invention can be designed in two ways to achieve the same paraboloid, the first is to meet the design requirements by adjusting the sector angles α1 ~ α8, and the second is to adjust the dihedral angle to meet the design requirements. The target paraboloid can be obtained by adding or removing material to the rigid thick plate of the rotating paraboloid-type foldable antenna structure, as shown in Fig. 10 and Fig. 11 .

本申请实施例中,可通过调整二面角的大小来制定曲面曲率。由于单自由度可展阵列截面形态类似梯度的形式在阶梯斜坡中上升,当截面倾角θ与抛物线倾角相似时,可以通过切割方法去除表面上多余材料,从而形成可展开结构的目标抛物线曲面,如图12所示,对均匀厚板的正面进行材料去除,背面不处理。该图12为天线结构沿中心线的剖面图,其中,除中心轮辐外,左右两侧的细实线与虚线代表结构中所有均匀厚板绕中心点划线一周所能到达的最高或最低位置,最高和最低位置中间有一个连续的空间区域,可以在这个区域中裁切出想要的抛物面。图12中粗实线介于上述空间区域中,为去除材料后的抛物面形状。In the embodiment of the present application, the curvature of the surface can be formulated by adjusting the size of the dihedral angle. Since the shape of the single-degree-of-freedom expandable array cross-section is similar to a gradient in the form of a ladder slope, when the cross-section inclination θ is similar to the parabola inclination, the excess material on the surface can be removed by cutting, thereby forming the target parabolic surface of the expandable structure, such as As shown in Figure 12, material removal is performed on the front side of a uniformly thick plate, and the back side is left untreated. Figure 12 is a cross-sectional view of the antenna structure along the center line, in which, except for the central spoke, the thin solid lines and dotted lines on the left and right sides represent the highest or lowest position that all uniform thick plates in the structure can reach around the center dotted line for one week , there is a continuous space area between the highest and lowest positions, and the desired paraboloid can be cut out in this area. In Fig. 12, the thick solid line intervenes in the above-mentioned space region, which is a parabolic shape after material removal.

本申请实施例中,所述单自由度折展阵列与中心的轮辐有两种连接方式,第一种是基本单元1的中间第二板(即图4、6中所示第八板2-8)的正面梯形底边与轮辐的正面边线相连,第二种是基本单元1的中间第二板(即图4、6中所示第八板2-8)的背面梯形底边与轮辐的正面边线相连;两种不同的装配方式形成两种不同的构型,分别为第一装配构型4-1以及第二装配构型4-2。In the embodiment of the present application, there are two connection modes between the single-degree-of-freedom folding array and the central spoke. The first is the middle second plate of the basic unit 1 (that is, the eighth plate 2- 8) The front trapezoidal base of the front is connected to the front side of the spoke, the second is the back trapezoidal base of the middle second plate of the basic unit 1 (that is, the eighth plate 2-8 shown in Figures 4 and 6) and the spoke. The front edges are connected; two different assembly methods form two different configurations, which are respectively the first assembly configuration 4-1 and the second assembly configuration 4-2.

在单自由度折展阵列同步运动的情况下,在第一装配构型中,展开至工作状态时呈现抛物面形状,收拢时轨迹呈单自由度运动,见图13左侧图;第二装配构型中,展开时呈现抛物面形状,收拢完成后,有图13中第二装配构型收拢后的两种不同状态,这两种状态之间可以相互转换,见图13右侧图。其中,第一装配构型与第二装配构型的单自由度折展阵列完全相同,区别在于折展阵列与中心轮辐的连接方式不同,第二装配构型中,在单自由度折展阵列折叠后,可以整体绕与轮辐相连的铰链翻折,第二装配构型收拢后的两种状态可看作翻折前后的两个状态。前述的两种装配形式在切割出抛物面时有所不同,第一种装配形式可以切割出较为完整的目标旋转抛物面,第二种装配形式不能完整的切割出抛物面。两种装配形式的折叠与展开状态如图13所示。In the case of synchronous movement of single-degree-of-freedom folding and unfolding arrays, in the first assembly configuration, when unfolded to the working state, it presents a parabolic shape, and when it is folded, the trajectory is a single-degree-of-freedom movement, as shown in the left side of Figure 13; the second assembly configuration In the model, it presents a parabolic shape when unfolded, and after being folded, there are two different states after the second assembly configuration in Figure 13 is folded, and these two states can be converted to each other, as shown in the right side of Figure 13. Among them, the single-degree-of-freedom folding arrays of the first assembly configuration and the second assembly configuration are exactly the same, the difference is that the connection mode of the folding array and the central spoke is different, in the second assembly configuration, the single-degree-of-freedom folding array After being folded, it can be folded integrally around the hinges connected to the spokes, and the two states after the second assembly configuration is folded can be regarded as two states before and after folding. The aforementioned two assembly forms are different in cutting out a paraboloid. The first assembly form can cut a relatively complete target rotating paraboloid, while the second assembly form cannot completely cut out a paraboloid. The folded and unfolded states of the two assembly forms are shown in FIG. 13 .

本申请实施例的旋转抛物面型可折展天线结构的具体工作过程如下:The specific working process of the rotating parabolic foldable antenna structure in the embodiment of the present application is as follows:

将本发明实施例的轮辐底面置于水平面,使单自由度折展阵列处于折叠状态,去掉人工压紧机构的干预后,其将在内置的弹簧驱动铰链的驱动下自行打开,展开到预期的工作位置后,厚板结构因干涉碰撞而停止进一步展开;在弹簧弹力和厚板板面接触力的作用下保持在预期工作型面位置。打开后,其整体将呈现出一个特定母线的抛物面,此时即为该抛物面型可折展结构的工作位置参见图14所示,图14示出了第一装配构型以及第二装配构型的一种收拢状态下的打开过程。展开结束后,可由人工或特定回收装置将阵列收拢,参见图13所示。Place the bottom surface of the spokes of the embodiment of the present invention on a horizontal plane, so that the single-degree-of-freedom folding array is in a folded state. After removing the intervention of the manual pressing mechanism, it will open automatically under the drive of the built-in spring-driven hinge, and unfold to the desired position. After the working position, the thick plate structure stops further expansion due to interference and collision; under the action of the spring force and the contact force of the thick plate surface, it remains at the expected working profile position. After opening, it will present a paraboloid with a specific generatrix as a whole, which is the working position of the paraboloid-shaped foldable structure. See Figure 14, which shows the first assembly configuration and the second assembly configuration An opening process in a folded state. After unfolding, the array can be folded up manually or by a special recovery device, as shown in Figure 13.

以上所述仅是本发明的优选实施方式,应当指出的是,对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下,还可以做出若干改进和润饰,这些改进和润饰也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, these improvements and Retouching should also be regarded as the protection scope of the present invention.

Claims (10)

1. The rotary paraboloid type foldable antenna structure is characterized by comprising a plurality of identical single-degree-of-freedom foldable arrays and a spoke, wherein the spoke is positioned in the middle of the foldable antenna structure, and the plurality of single-degree-of-freedom foldable arrays are distributed at certain angles around the center line of the spoke; the single-degree-of-freedom folding and unfolding array is formed by alternately arranging a plurality of basic folding and unfolding units, and each basic folding and unfolding unit is formed by connecting rigid thick plates through a first spring driving hinge; each single-degree-of-freedom folding array is connected with the spoke through a second spring driving hinge; when the foldable antenna structure is unfolded to a working state, the side edges of the single-degree-of-freedom foldable array correspond to each other; the surface morphology of the rigid thick plate is subjected to material adding and cutting treatment, and a dihedral angle or a sector angle is adjusted to make a curved surface curvature, so that the rigid thick plate has a preset molded surface to meet the molded surface and self-locking requirements.
2. The rotating parabolic dish type foldable antenna structure according to claim 1, wherein the structures of the plurality of single degree of freedom foldable arrays are identical.
3. The rotating parabolic foldable antenna structure according to claim 1, wherein the single degree of freedom foldable array is composed of a first basic foldable unit, a second basic foldable unit, and a third basic foldable unit; the first basic folding and unfolding units are symmetrically arranged next to the spokes and are sequentially arranged; the second basic folding and unfolding units are arranged above the first basic folding and unfolding units; the third basic folding and unfolding unit is positioned between the first basic folding and unfolding unit and the second basic folding and unfolding unit, and the first basic folding and unfolding unit and the second basic folding and unfolding unit are arranged in a staggered manner and share the rigid thick plate.
4. The structure of claim 1, wherein when the single degree of freedom folded array is unfolded into a plane and the number of columns of the rigid thick plates is determined, the number of arrays is calculated by adjusting the size of the fan-shaped angle, so that a plurality of the single degree of freedom folded arrays are unfolded to form a closed loop, thereby making a curvature of a curved surface.
5. The rotating parabolic type foldable antenna structure according to claim 1, wherein when the dihedral angle of the single degree of freedom foldable array is determined, the curvature of the curved surface is formulated by adjusting the magnitude of the dihedral angle.
6. The rotating parabolic dish type foldable antenna structure according to claim 1, wherein a front trapezoid base/a rear trapezoid base of a middle lower plate of the basic folding unit of the single degree of freedom folding array is connected with a front side line of a spoke to form a first assembling configuration and a second assembling configuration respectively.
7. The rotating parabolic dish-type foldable antenna structure according to claim 6, wherein the front trapezoid base of the intermediate lower plate of the basic folding unit is connected to the front side line of the spoke to form a first assembly configuration; the first assembly configuration is in a shape of a paraboloid of revolution when being unfolded to a working state when the single-degree-of-freedom folded array synchronously moves, and a complete target paraboloid of revolution is cut out, and a track moves in a single degree of freedom when being folded.
8. The rotating parabolic dish-type foldable antenna structure according to claim 6, wherein the front trapezoid base of the intermediate lower plate of the basic folding unit is connected to the back side line of the spoke to form a second assembly configuration; the second assembly configuration presents a parabolic shape when unfolded when the single-degree-of-freedom folding array moves synchronously, and has two different states after the folding is completed, and the two states can be mutually converted.
9. The structure of claim 1, wherein the profile of the rigid plank is matched with the target paraboloid by removing material, and the rigid plank is contacted with the adjacent rigid plank when being unfolded to the working position by adding material, so that the single-degree-of-freedom folding array can be kept in the working position under the combined action of the contact force between the spring driving hinge and the rigid plank, and the profile of the rigid plank is matched with the target paraboloid, so that the rotating paraboloid type folding structure with large folding ratio, high profile precision and high stability is formed.
10. The structure of claim 1, wherein the single degree of freedom deployable array has a cross-sectional shape that rises in a gradient fashion in a stepped slope, and when the cross-sectional tilt matches the parabolic tilt, the profile of the rigid slab is matched to the target parabola by removing and adding material to the rigid slab.
CN202310525937.XA 2023-05-11 2023-05-11 Rotary paraboloid type foldable antenna structure Pending CN116632509A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118431746A (en) * 2024-04-28 2024-08-02 长春理工大学中山研究院 Antenna dielectric constant modulation device and reconstruction method based on 3D printing technology

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118431746A (en) * 2024-04-28 2024-08-02 长春理工大学中山研究院 Antenna dielectric constant modulation device and reconstruction method based on 3D printing technology

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